Super-Micro has 36 and 72 drive racks that aren't horrible human effort wise (you can get 90 drive racks, but I wouldn't recommend it). You COULD get 8TB drives for like 9.5 cent / GB (including the $10k 4U chassi overhead). 4TB drives will be more practical for rebuilds (and performance), but will push you to near 11c / GB. You can go with 1TB or even 1/2TB drives for performance (and faster rebuilds), but now you're up to 35c / GB.
That's roughly 288TB of RAW for say $30k 4U. If you need 1/2 PB, I'd say spec out 1.5PB - thus you're at $175K .. $200k.. But you can grow into it.
Note this is for ARCHIVE, as you're not going to get any real performance out of it.. Not enough CPU to disk ratio.. Not even sure if the MB can saturate a 40Gbps QSFP links and $30k switch. That's kind of why hadoop with cheap 1CPU + 4 direct-attached HDs are so popular.
At that size, I wouldn't recommend just RAID-1ing, LVMing, ext4ing (or btrfsing) then n-way foldering, then nfs mounting... Since you have problems when hosts go down and keeping any of the network from stalling / timing out.
Note, you don't want to 'back-up' this kind of system.. You need point-in-time snapshots.. And MAYBE periodic write-to-tape.. Copying is out of the question, so you just need a file-system that doesn't let you corrupt your data. DEFINITELY data has to replicate across multiple machines - you MUST assume hardware failure.
The problem is going to be partial network down-time, crashes, or stalls, and regularly replacing failed drives.. This kind of network is defined by how well it performs when 1/3 of your disks are in 1-week-long rebuild periods. Some systems (like HDFS) don't care about hardware failure.. There's no rebuild, just a constant sea of scheduled migration-of-data.
If you only ever schedule temporary bursts of 80% capacity (probably even too high), and have a system that only consumes 50% of disk-IO to rebuild, then a 4TB disk would take 12 hours to re-replicate. If you have an intelligent system (EMC, netapp, ddn, hdf, etc), you could get that down to 2 hours per disk (due to cross rebuilding).
I'm a big fan of object-file-systems (generally HTTP based).. That'll work well with the 3-way redundancy. You can typically fake out a POSIX-like file-system with fusefs.. You could even emulate CIFS or NFS. It's not going to be as responsive (high latency). Think S3.
There's also "experimental" posix systems like ceph, gpfs, luster. Very easy to screw up if you don't know what you're doing. And really painful to re-format after you've learn it's not tuned for your use-case.
HDFS will work - but it's mostly for running jobs on the data.
There's also AFS.
If you can afford it, there are commercial systems to do exactly what you want, but you'll need to tripple the cost again. Just don't expect a fault-tolerant multi-host storage solution to be as fast as even a dedicated laptop drive. Remember when testing.. You're not going to be the only one using the system... Benchmarks perform very differently when under disk-recovery or random-scatter-shot load by random elements of the system - including copying-in all that data.